Constrained Trading Networks

TL;DR

This paper models trading networks with bilateral contracts using network theory, incorporating polymatroidal constraints to represent substitution limits, and analyzes the existence of competitive equilibria in multi-sided markets.

Contribution

It extends existing models by introducing polymatroidal constraints and analyzes equilibrium existence in multi-sided trading networks.

Findings

Existence of competitive equilibrium in two-sided markets.

Non-existence of equilibrium in some multi-sided markets.

Modeling of substitution limits via polymatroidal constraints.

Abstract

Trades based on bilateral (indivisible) contracts can be represented by a network. Vertices correspond to agents while arcs represent the non-price elements of a bilateral contract. Given prices for each arc, agents choose the incident arcs that maximize their utility. We enlarge the model to allow for polymatroidal constraints on the set of contracts that may be traded which can be interpreted as modeling limited one for-one substitution. We show that for two-sided markets there exists a competitive equilibrium however for multi-sided markets this may not be possible.